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Abstract

Correlation dependent, propagation-induced shifts in the generalized spectra of cyclostationary, random fields are predicted. This result generalizes the Wolf shift for stationary fields and is applicable to periodic trains of fast pulses such as might be generated in comb spectroscopy or other mode-locked pulsed systems. Examples illustrate these shifts for intrinsically stationary fields and the fields generated by a mode-locked laser.

Figures (1)

(Color online) The normalized spectral density C̃0(ω) and the spectral correlation function |C̃4(ω|) normalized by its peak, at the source (dashed lines in red) and at a point in the far zone P = (100,0,12000) mm (shown in black) for the case when there are three sources, located at (−100,0,0) mm, (0,0,0) mm, and (100,0,0) mm. The peak of C̃0(ω) is at a higher frequency than the peak of |C̃4(ω)|. The top two panels contain plots of C̃0 and |C̃4| for a three-source system with μ = 0.8, the repetition frequency is taken to be 5×1013 rad/s, the bandwidth of the coherence and the bandwidth of the spectrum are both 20% of
̃ the center frequency ωc = 5×1015 rad/s. The middle two panels contain plots of C̃0 and |C̃4| for the same three-source system as above, only with μ= 0.1. The bottom two panels contain plots of C̃0 and |C̃4| for a three-source system that differs from the one in the middle panels by changing the repetition frequency from 5 ×1013 rad/s to 2.5×1014 rad/s.